4D Geomechanics
Learning objectives
- Explain the 4D time-shift: depletion compacts the reservoir, strains the overburden, and shifts the seismic travel time
- Apply the Hatchell-Bourne R-factor: the fractional time shift is one plus R times the vertical strain
- Read a few-millisecond time-shift on a baseline-monitor trace pair and invert it back to the strain
- Connect 4D geomechanics to the Rock Physics and Synthetic Seismic time-lapse treatments
Watching the Reservoir from the Surface
The stress path, the subsidence bowl, and the casing shear were all consequences of compaction. This section reads compaction the way the industry most often does, with repeated seismic. Shoot a survey, produce the field, shoot it again, and subtract: the difference, the 4D or time-lapse signal, images the change. Compaction shows up as a time shift. As the reservoir shortens, the overburden above it is pulled down and stretched, its velocity drops, and the seismic reflection from below the reservoir arrives later. A reflector that has not physically moved appears to shift down in time, and that shift is the fingerprint of the compaction above it.
The Hatchell-Bourne (2005) relation puts a number on it: the fractional time shift is , where is the vertical strain of the layer and is the R-factor, the ratio of the fractional velocity change to the fractional length change. R is not one. Rock velocity is more sensitive to strain than length is, so R runs from about 2 to 5, and the time shift is amplified several-fold over the pure geometric stretch. A stiff reservoir writes a sub-millisecond shift; a soft, thick chalk depleted hard writes several milliseconds, small but robustly measurable with modern repeatable surveys.
The R-Factor Carries the Physics
The R-factor is where the rock physics lives. It encodes how much the overburden's velocity softens per unit stretch, which depends on the rock, its stress sensitivity, and its fluids, exactly the stress-dependent velocity of the Rock Physics course. A stiff, stress-insensitive overburden has a low R and a muted 4D signal; a soft, stress-sensitive one has a high R and a loud signal. Invert the measured time shift with the right R and you recover the strain, and from the strain the compaction, and from the compaction the pressure change, a chain from a surface seismic difference all the way down to the reservoir pressure. Move the R-factor and watch the same compaction write a larger or smaller shift; this is why calibrating R, against the subsidence bowl or a compaction log, is the crux of quantitative 4D geomechanics. The sign carries information too: overburden stretch gives a positive time shift, a slowdown, while the reservoir's own compaction gives a negative one, a speedup confined to the reservoir interval, and the pattern of shifts across the survey maps where the pressure has changed and where it has not, drainage and compartments made visible.
One Compaction, Four Faces
The producing field has now shown compaction four ways: the stress path that starts it, the subsidence bowl at the surface, the casing shear in the wells, and the 4D time shift in the seismic. They are one physical process, reservoir compaction under the stress path, read on four instruments. The Rock Physics course reads the same 4D signal from the velocity side (rp_8_6) and the Synthetic Seismic course models it forward (smk_8_2); geomechanics supplies the strain both of those convert to a seismic difference. With the producing field mapped, Part 10 turns to two capstones that put the whole course to work on a single failing well.
References
- Hatchell, P., & Bourne, S. (2005). Rocks under strain: strain-induced time-lapse time shifts are observed for depleting reservoirs. The Leading Edge, 24(12), 1222-1225.
- Barkved, O. I., & Kristiansen, T. (2005). Seismic time-lapse effects and stress changes: examples from a compacting reservoir. The Leading Edge, 24(12), 1244-1248.
- Herwanger, J., & Horne, S. A. (2009). Linking reservoir geomechanics and time-lapse seismics. Geophysics, 74(4), W13-W33.